Quadratic finite-volume methods for elliptic and parabolic problems on quadrilateral meshes: Optimal-order errors based on Barlow points

Min Yang, Jiangguo Liu, Yanping Lin

Research output: Journal article publicationJournal articleAcademic researchpeer-review

7 Citations (Scopus)

Abstract

This paper presents quadratic finite-volume methods for elliptic and parabolic problems on quadrilateral meshes that use Barlow points (optimal stress points) for dual partitions. Introducing Barlow points into the finite-volume formulations results in better approximation properties at the cost of loss of symmetry. The novel 'symmetrization' technique adopted in this paper allows us to derive optimal-order error estimates in the H1-and L2-norms for elliptic problems and in the L∞ (H1)-and L∞ (L2)-norms for parabolic problems. Superconvergence of the difference between the gradients of the finite-volume solution and the interpolant can also be derived. Numerical results confirm the proved error estimates.
Original languageEnglish
Pages (from-to)1342-1364
Number of pages23
JournalIMA Journal of Numerical Analysis
Volume33
Issue number4
DOIs
Publication statusPublished - 1 Oct 2013

Keywords

  • Barlow points
  • elliptic boundary value problems
  • error estimation
  • finite-volume element methods
  • parabolic equations
  • quadrilateral meshes

ASJC Scopus subject areas

  • Mathematics(all)
  • Computational Mathematics
  • Applied Mathematics

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